How do you know an exponential expression will eventually be larger than any quadratic expression?
Answer:
when the base is larger than 1"
Step-by-step explanation:
"How do you know an exponential expression will be larger than any quadratic expression?" The answer for that would be: "An exponential expression will be larger than any quadratic expression when the base is larger than 1"
2x-3y+z=0
3x+2y=35
4y-2z=14
Which of the following is a solution to the given system?
A. (2, 3, 5)
B. (3, 2, 0)
C. (1, 16, 0)
D. (7, 7, 7)
Based on the evaluations, only Option D: (7, 7, 7) satisfies all three equations and is a solution to the given system.
To determine which of the given options is a solution to the system of equations, we can substitute the values into the equations and check if they satisfy all three equations simultaneously. Let's evaluate the options one by one:
Option A: (2, 3, 5)
Checking the equations:
2(2) - 3(3) + 5 = 4 - 9 + 5 = 0 (satisfies the first equation)
3(2) + 2(3) = 6 + 6 = 12 (does not satisfy the second equation)
4(3) - 2(5) = 12 - 10 = 2 (does not satisfy the third equation)
Option B: (3, 2, 0)
Checking the equations:
2(3) - 3(2) + 0 = 6 - 6 + 0 = 0 (satisfies the first equation)
3(3) + 2(2) = 9 + 4 = 13 (does not satisfy the second equation)
4(2) - 2(0) = 8 - 0 = 8 (does not satisfy the third equation)
Option C: (1, 16, 0)
Checking the equations:
2(1) - 3(16) + 0 = 2 - 48 + 0 = -46 (does not satisfy the first equation)
3(1) + 2(16) = 3 + 32 = 35 (satisfies the second equation)
4(16) - 2(0) = 64 - 0 = 64 (does not satisfy the third equation)
Option D: (7, 7, 7)
Checking the equations:
2(7) - 3(7) + 7 = 14 - 21 + 7 = 0 (satisfies the first equation)
3(7) + 2(7) = 21 + 14 = 35 (satisfies the second equation)
4(7) - 2(7) = 28 - 14 = 14 (satisfies the third equation)
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6. Mr. Johnson sells and repairs watches at his store. Part A: Mr. Johnson took the price of a watch that was listed at $60 and marked it up by 30%. After the markup, what is the selling price of the watch?
Answer:
$78.
Step-by-step explanation:
Listing price of watch = $60
Given that the watch price was marked up by 30%,
lets find 30% of listing price to find increase in price after mark up
30% of listing price = 30/100 * $60 = $18
Thus,
New selling price = Listing price of watch + marked up price
New selling price = $60 + $18 = $78
Thus, new selling price after mark up is $78.
A cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F. The table shows temperature readings for the cake.
b. How long does it take the cake to cool to the desired temperature?
A cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F. The table shows temperature readings for the cake.
b. How long does it take the cake to cool to the desired temperature?
To determine how long it takes the cake to cool to the desired temperature, we need to have additional information about the rate at which the cake cools down.
The time it takes for the cake to cool depends on various factors such as the ambient temperature, the size and shape of the cake, the type of pan used, and the insulation around the cake. Without this information, it is not possible to accurately calculate the exact time it takes for the cake to cool to 120⁰F.
In general, the cooling process can be influenced by factors such as room temperature, air circulation, and the thickness of the cake. A larger or thicker cake may take longer to cool compared to a smaller or thinner cake.
If you have access to a cake cooling chart or if the recipe provides specific instructions on the cooling time, you can refer to that information to estimate the time it takes for the cake to cool.
Otherwise, it may be necessary to monitor the cake's temperature periodically and use your judgment to determine when it has reached the desired temperature of 120⁰F.
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A cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F. The table shows temperature readings for the cake.
b. How long does it take the cake to cool to the desired temperature?
True or False: The graph below represents the table of values.
Answer:
False
Step-by-step explanation:
I would say false;
This graph is really hard to read because of the way it's subdivided but one of the coordinate points is (0,-1) and the line clearly passes through the origin (0,0).
If you have the chance, please tell your teacher to provide better graphs that are actually readable.
Which of the following are factors of 11?
A/1
B/11
C/4
D/5
E/0
F/22
Answer:
B, F
Chow,...!
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Range ($)
Progressive
Tax Rate
0-3000
2%
3001 - 5000
3%
5001 - 17,000
5%
17,001 and up
5.75%
Calculate the state income tax owed on a $60,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter
The state income task owed on a salary of $60,000 per year according to the given ranges is; $3,450.
What is the state income tax owed by the $60,000 per year?It follows from the task content that for incomes of 17, 001 and above, the tax rate is; 5.75% .
Hence, it follows that for an individual whose in one is $60,000 per year, the state income tax owed is;
Tax = 5.75% of $60,000
= $3,450
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Ms. Hamm bought a new car for $37,500. It is said that her car depreciates at a rate of 7% each year
Answer:
This would mean that the next year her car's value would go down by $2,625. The new value of the car would consequently be $34,875.
Step-by-step explanation:Here is how you can solve this problem:
Okay, so first, let's find 7% of $37,500. To do this, the simple way would be to find first 1% of $37,500. 1% of $37,500 is $375. This is because you are moving the decimal point two spaces to the left.Now that we know that 1% of $37,500 is $375, let's multiply this value by 7.
375 x 7 = 2625.Subtract 2625 from 37,500.You will get $34,875.Let's say that the next year, her car value goes down by 7% again.
THIS IS THE IMPORTANT PART:
YOU FIND 7% OF THE NEW VALUE, NOT $37,500. YOU WOULD FIND 7% OF $34,875.
Hope this helps! :)
can someone please help?? what’s the measure of the vertex angle
Answer:
120 deg
Step-by-step explanation:
There is an angle symbol in the equilateral triangle and another symbol in half of the vertex angle. Those two angles are congruent.
The measure of the vertex angle is 2 * 60 deg = 120 deg
Answer: 120 deg
Help I have 1 more try. Need answer
Answer:12
Step-by-step explanation:2/5=0.4
0.4x30=12
Answer: 12
Step-by-step explanation:
1. Multiply Across the Top: 2 x 30 = 60
2 Divide 60 / 5 = 12
In the picture:
There are equal 5 sections in 30.
So 30/5 = 6 and each section represents "6".
Since the question is asking about 2 of the sections it is 6+6 which is 12.
remake of steps to graph a line, if equation is 2x+4y=8
Answer: slope is -1/2 y intercept is (0,2)
Step-by-step explanation: How I Got This Was Using The Slope Formula Y = mx + b to find slope then graphed by using those two points
Find the lettered angles in each of the following (see image ).
Sorry for the wobbly drawing.
please show workings.
Answer:
x = 252°, y = 126° , z = 54°
Step-by-step explanation:
( Hopefully I've read the size of the angle 126° correctly )
The central angle x is twice the inscribed angle, that is
x = 2 × 126° = 252°
∠ y = 126° ( angles on the circumference subtended by the same arc )
y and z are adjacent angles and are supplementary , that is
y + z = 180°
126° + z = 180° ( subtract 126° from both sides )
z = 54°
The mathematical constant pi is needed when calculating the area of a
When computing the area of a circle, the mathematical constant pi () is required. Pi is the circumference-to-diameter ratio of a circle and is approximately equal to 3.14159.
The area of a circle is calculated by multiplying pi by the radius squared (r2). To estimate the area of a circle, utilize pi in the calculation since it is a vital aspect of the relationship between the circumference and diameter of a circle.
Pi is not required when determining the area of a square, rectangle, or cube since the formulas for these shapes are different.
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The question is -
The mathematical constant pi is needed when calculating the area of a _.
a. circle
b. square
c. rectangle
d. cube
Find the surface area of the cap cut from the paraboloid z = 2 - x² - y² by the cone z = √x² + y²
To find the surface area of the cap cut from the paraboloid by the cone, we need to calculate the surface area of the intersection between the two surfaces.
To find the region of intersection, we equate the equations of the paraboloid and the cone: 2 - x² - y² = √(x² + y²)Simplifying this equation, we have: x² + y² + √(x² + y²) - 2 = 0 This equation represents the boundary of the region of intersection. By solving this equation, we can determine the bounds for the variables x and y.
Once we have the region of intersection, we can calculate the surface area by evaluating the surface integral over this region. The formula for the surface area of a surface S is given by:
A = ∬S √(1 + (dz/dx)² + (dz/dy)²) dA
In this case, we need to express the surface in terms of the variables x and y and then calculate the partial derivatives dz/dx and dz/dy. After that, we can evaluate the double integral over the region of intersection to find the surface area of the cap cut from the paraboloid by the cone.
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Which statement is true about function f, which is shown in the graph? f(x) -8x⁵+ 4x³+5x?
A. Function f is neither even nor odd.
B. Function f is even.
C. Function f is odd.
D. function f is both even and odd.
Answer:
f(-x)=-f(x)
So, Function f is odd
Option C is correct.
Step-by-step explanation:
Which statement is true about function f, which is shown in the graph?
f(x)= -8x⁵+ 4x³+5x?
Function is even if f(-x)= f(x)
and function is odd if f(-x)=-f(x)
Putting x=-x and finding f(-x)
f(-x)=-8(-x)^5+4(-x)^3+5(-x)
f(-x)=-8(-x^5)+4(-x^3)-5x
f(-x)=+8x^5-4x^3-5x
f(-x)=-(-8x^5+4x^3+5x)
f(-x)=-f(x)
So, Function f is odd
Option C is correct.
The function f(x) = -8x⁵+ 4x³+5x is an odd function option (C) Function f is odd is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = -8x⁵+ 4x³+5x
Plug x → -x
f(-x) = -8(-x)⁵+ 4(-x)³+5(-x)
f(-x) = 8x⁵- 4x³-5x
f(-x) = -( -8x⁵+ 4x³+5x)
f(-x) = -f(x) (condition for odd function)
Thus, the function f(x) = -8x⁵+ 4x³+5x is an odd function option (C) Function f is odd is correct.
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how to find domain and range of math function?
The domain are all of the x-values that are located on the x-axis of a cartesian coordinate while the range all of the y-values that are located on the y-axis of a cartesian coordinate.
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
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Simplify the following expressions and write all answers with positive exponents and no radicals.
Given:
Expression is
\(\frac{6ab^3}{(6b)^3}\)Required:
Simplify the following expression.
Explanation:
We will simplify as
\(\begin{gathered} =\frac{6ab^3}{(6b)^3} \\ =\frac{a}{36} \end{gathered}\)Answer:
Hence, above is the expression.
determine the number and type of solutions for each equation fundamental theorem of algebra
To determine the number and type of solutions for a specific equation, we need to consider the degree of the polynomial and use other mathematical techniques.
1. Linear Equation (degree 1):
A linear equation in one variable has exactly one solution, regardless of whether the coefficients are real or complex.
2. Quadratic Equation (degree 2):
A quadratic equation in one variable can have zero, one, or two solutions. The nature of the solutions depends on the discriminant (b² - 4ac), where a, b, and c are the coefficients of the equation.
- If the discriminant is positive, the equation has two distinct real solutions.
- If the discriminant is zero, the equation has one real solution (a double root).
- If the discriminant is negative, the equation has two complex solutions.
3. Cubic Equation (degree 3):
A cubic equation in one variable can have one, two, or three solutions. To determine the nature of the solutions, it often requires advanced algebraic techniques, such as factoring, the Rational Root Theorem, or Cardano's method.
4. Higher-Degree Equations (degree 4 or higher):
Equations of higher degree can have varying numbers of solutions, but there is no general formula to determine them. Instead, various numerical methods, such as numerical approximation or graphing techniques, are commonly used to estimate the solutions.
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can someone help me with this?
Answer:
12.1 cm
Step-by-step explanation:
Did I divided the polinoms in a correct way?
If I didn't please explain how
Answer:
siesta bien
Step-by-step explanation:
A coupon bond which pays interest of $60 annually, has a par value of $1,000, matures in 5 years, and is selling today at a $75.25 discount from par value. The current yield on this bond is:
A. 6.00%
B. 6.49%
C. 6.73%
D. 7.00%
The current yield on this bond is 6.49%.
A bond's yearly interest payment, market price, and par value must be known in order to determine the bond's current yield.
In this question, we are given that the bond pays an annual interest of $60, has a par value of $1,000, and is selling at a $75.25 discount from par value.
So, the market price of the bond is the par value minus the discount, which is \($ 1,000\) - \($75.25\) \(= $924.75.\)
To calculate the current yield, we use the formula:
Current Yield \(=\) (Annual Interest Payment / Current Market Price) x 100%
With our current values substituted, we obtain:
Current Yield \(= ($60 / $924.75) × 100%\)
Current Yield \(= 0.0649 × 100%\)
Current Yield \(= 6.49%\)%
Therefore, (B) 6.49% is the right response.
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find the nth term - 8,14,20,26
how would you solve 8=2x+88?
Answer:
-40
Step-by-step explanation:
Let me know if you have any more questions
\(\huge\text{Hey there!}\)
\(\mathsf{8 = 2x + 88}\\\mathsf{2x + 88 = 8}\\\large\text{Subtract 88 to both sides}\\\mathsf{2x + 88 - 88 = 8 - 88}\\\large\text{Simplify it:}\\\mathsf{2x = 8 - 88}\\\mathsf{2x = -80}\\\large\text{Divide 2 to both sides:}\\\mathsf{\dfrac{2x}{2} = \dfrac{-80}{2}}\\\large\text{Simplify it:}\\\mathsf{x = \dfrac{-80}{2}}\\\\\mathsf{x = -40}\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{x = -40}}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
430 were sold.
4.25 for soda
5.50 for popcorn
the total is 2077.50
how many of each were sold?
Answer:
Soda = 230
Popcorn = 200
Step-by-step explanation:
(4.25 x 230) + (5.50 x 200) = 2,077.50
230 + 200 = 430
6. A line passes through the points (-2,5) and (6,9). Calculate the gradient of this line.
Answer:
d 2.5 line is 6.9 which is 9.4
Step-by-step explanation:
because
A football is kicked from a point on the ground such that its height h(t), in feet, is given by the
equation h(t)=-16x² +80 t, where t is time in seconds. Find the average rate of change in
the height of the ball from when it reaches its maximum height until it reaches the ground
Hence , the average rate of change in the height of the ball from when it reaches its maximum height until it reaches the ground is -32x +80 .
In arithmetic, Differentiation will be outlined as a by-product of a operate with relevance associate degree variable quantity.Differentiation, in calculus, will be applied to live the operate per unit amendment within the variable quantity.We have given an equation h(t)=-16x² +80 t . .....(1)
Differentiating equation (1) with respect to t , we get
h'(t) = -16 ×2x +80
= -32x +80
It is given that ball reaches its maximum height which means that
h'(t) =0
-32x +80 = 0
-32x = -80
x = 80 /32
x =2.5
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The cost (in dollars) of a basic music streaming service for m months
is represented by B(m) = 5m. The cost of the premium service is represented by
P(m) 10m. Describe the transformation from the graph of B to the graph of P.
The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2
How to determine the transformation?From the question, the function definitions are given as
B(m) = 5m
P(m) = 10m
Rewrite the function P(m) as follows
P(m) = 2 x 5m
Substitute B(m) = 5m in the equation P(m) = 2 x 5m
P(m) = 2 x B(m)
When a function is represented as
f(x) = kg(x), then the transformation is a vertical stretch by k
Hence. the transformation a vertical stretch by 2
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_____ show the change in one or more variables progressively across time. a. Histograms b. Pie charts c. Line graphs d. Bar charts e. Diagrams.
The correct answer is c. Line graphs show the change in one or more variables progressively across time.
Histograms show the distribution of data, pie charts show the proportions of a whole, bar charts compare categories or groups, and diagrams show the relationships between different elements.
The correct answer is c. Line graphs show the change in one or more variables progressively across time
A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighbouring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics. Frequency, which can be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data.
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Line graphs show the change in one or more variables progressively across time. C
A line graph is a type of chart that displays data as a series of data points connected by straight lines.
The horizontal axis of the graph typically represents time, while the vertical axis represents the value of the variable being measured.
By connecting the data points with lines, a line graph can show the trend or pattern of change in the variable over time.
Line graphs are commonly used in fields such as economics, finance, and science to visualize trends in data over time.
They can be used to identify patterns, compare different variables, or forecast future trends.
In contrast, histograms, pie charts, bar charts, and diagrams are different types of charts that are used to display data in different ways.
Histograms are used to show the distribution of data within a single variable, while pie charts and bar charts are used to compare different categories or groups of data.
Diagrams are used to represent complex systems or relationships, often using visual symbols or icons to represent different components.
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Explain how an enlargement or a reduction In the dimensions of a building would cause a change in the scale factor
Answer:
The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship.
Step-by-step explanation:
Hope it helps XD
Answer:
The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship.
Step-by-step explanation:
Typically, a continuous random variable is one whose value is determined by measurement instead of counting. (True or false)
The Statement asked based on the Variable is , True.
What is Variable?A variable is a symbol or letter that represents a quantity or value that can vary or change in a given context or problem. Variables can be used to express relationships between quantities or to describe patterns or trends in data. They can be either dependent or independent, depending on the context of the problem. An independent variable is a variable that is changed or controlled by the experimenter or observer, while a dependent variable is a variable that is affected or influenced by the independent variable.
True.
A continuous random variable is one that can take on any value within a certain range or interval, and its value is determined by measurement. Examples of continuous random variables include height, weight, temperature, and time, where the values can be any real number within a certain range.
In contrast, a discrete random variable can only take on certain values, typically integers, and its value is determined by counting. Examples of discrete random variables include the number of heads in a series of coin tosses, the number of cars sold in a day, and the number of defects in a batch of products.
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